00:01
So we're looking at revenue, given these three different marketing plans, market plan, one, two, and three.
00:09
And these are the revenues.
00:10
And we want to find if the mean revenues are different under these marketing plans.
00:18
So this is a perfect setup for a one -way an nova.
00:21
So you take your data and you run it through anova, which you initially get your summary statistics.
00:26
So groups 1, 2, and 3, the marketing plans, 1, 2, and 3.
00:30
There's a toll of 60 observations, 60 customers, and here's these sums, the means, here's the mean of each and the variance.
00:40
And as we look at the means, we notice they're not all the same, and the question is, is that significant? and they significantly different from each other.
00:49
Because the way the hypothesis, or the anova works, is you assume the null hypothesis, is that the mean of them of the three are the same.
01:00
The means are all the same.
01:03
The alternative is that they're not all the same.
01:06
The means are not all the same.
01:17
And then we test this against some alpha, some preset alpha value.
01:25
And we're not told which one to use.
01:26
So i'm just going to use a standard one of alpha 0 .05.
01:29
And that means we reject the null hypothesis if our p value is less than this alpha.
01:35
So we run the anova.
01:38
And we find the f statistic is this large value, 51 .8s against a crue.
01:42
Critical value of 3 .15 and 3 .16 and the p values for all intensive purposes zero.
01:48
So we reject the hypothesis and we say the means are not all equal.
01:53
But now the question is, okay, now that we know that, which marketing plan do we use? so there's a few ways to go about doing this and i'll show you all of them.
02:04
The visual way, which i think is what a lot of people might lean to because it's easy to see.
02:14
So we're looking at them all.
02:15
Now, here's market plan one, two, and three.
02:19
This is a box plots where the medians are given here, not as opposed to the means.
02:25
But this shows you the spread of the data, which is useful to see.
02:29
And if you're looking at one, it was what, 3 ,200, so here's 3 ,000.
02:33
So the mean and median are not exact, but pretty close.
02:38
The second one is 6 ,100.
02:41
So 61, the mean is actually gonna be more about here as opposed to the median, which is down here.
02:46
Here.
02:48
And then the third one, we've got 8300.
02:52
There's nine.
02:54
So the median is about 9 ,000, whereas the mean is going to be a little lower than that.
02:59
So here's the, here's the mean right here.
03:02
So here's x bar three, x bar two, and then here's x bar.
03:07
X bar one is almost the same as the median.
03:10
And so this shows they're not perfectly symmetric, but relatively symmetric.
03:14
And they're all spread out the same, more or less.
03:17
I mean, this one looks like it's a little more, a little less variance because you have 50 % in this wider, in this narrower range, whereas these two is a bit wider variation...